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arXiv 2103.02837quant-ph
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状态集与幺正信道的量子证明

Quantum certification of state set and unitary channel

Wei Xie

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11 pages
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摘要：

研究了量子态集和幺正量子信道的有效量子认证算法。我们提出了一种算法，使用$O(\varepsilon^{-4}\ln |\mathcal{P}|)$副本的一个未知的状态，以区分是否包含在或$\varepsilon$的未知状态-远离一个有限的集合$\mathcal{P}$的已知状态相对于跟踪距离。该算法在某些设置中更具有采样效率。以前的研究表明，人们可以区分一个未知的酉$U$是否等于或$\varepsilon$ -远离一个已知的或未知的酉$V$在固定的维度与$O(\varepsilon^{-2})$使用的酉，其中使用的Choi状态，因此需要一个辅助系统。我们给出了一种算法，该算法通过$O(\varepsilon^{-1})$使用酉变换来区分这两种情况，与以前的结果相比，使用更少或不使用辅助变换。

英文摘要：

We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown state is contained in or $\varepsilon$-far from a finite set $\mathcal{P}$ of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $\varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(\varepsilon^{-2})$ uses of the unitary, in which the Choi state is used and thus an ancilla system is needed. We give an algorithm that distinguishes the two cases with $O(\varepsilon^{-1})$ uses of the unitary, using much fewer or no ancilla compared with previous results.

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